A Guide to the Mathematics of Map Projections
A technical paper (47 pages) on the mathematics of map projections with particular emphasis on the transverse Mercator projection and Redfearn’s equations. This paper was presented at the Victorian Tasmanian Survey Conference: Across the Strait, Launceston, Tasmania, 15-17 April, 2004.
A GUIDE TO MAP PROJECTIONS V3.pdf
Map Projection Theory
Lecture notes on the theory of map projections (two parts, 41 + 10 pages).
MapProjectionTheory_1.pdf
MapProjectionTheory_2.pdf
Minimum-Error Equal-Area Pseudocylindrical Map Projection
A technical paper published in Cartography and Geographic Information Systems,( Vol. 17, No. 2, 1990, pp.161-167). The point pole of a pseudocylindrical map projection may be expanded to a line to alleviate distortions in the map at high latitudes. The ration between pole length and equator length may be determined so as to give a minimum-error pseudocylindrical map projection. A variation of the minimum-error technique, as proposed by Sir George Airy, is applied to the sinusoidal projection to demonstrate the method.
Minimum Error Deakin 1990.pdf
Minimum Error Map Projection for Victoria
A technical paper presented at the FIG XX International Conference (Commission 5), Melbourne, Victoria, 5-12 March, 1994 (13 pages)
Minimum Error projection for Victoria.pdf
Some Applications of Clenshaw’s Recurrence Formula in Map Projections
A technical paper (34 pages) providing a detailed discussion of Clenshaw’s recurrence formula and associated summation algorithm with applications in map projections. In particular, computation of meridian distance on the ellipsoid and transformations between the ellipsoid and the Transverse Mercator projection. Matlab functions included.
Clenshaw_Map_Projections_V2.pdf
The Gauss-Krüger Projection
A technical paper (20 pages) by R.E. Deakin, M.N. Hunter and C.F.F. Karney on the Gauss-Krüger projection and Krüger’s equations (series method). This paper was presented at the 23rd Victorian Regional Survey Conference, Warrnambool, 10-12 September, 2010.
Gauss-Krueger Warrnambool Conference V2.pdf
The Gauss-Krueger Projection: Karney-Krueger equations
A technical paper (22 pages) by R.E. Deakin, M.N. Hunter and C.F.F. Karney on the Gauss-Krueger projection and the Karney-Krueger equations. This paper was presented at the 25th International Cartographic Conference, Paris, 3-8 July, 2011.
Gauss-Krueger Paris Conference V2.pdf
A Fresh Look at the UTM Projection: Karney-Krueger equations
A technical paper (19 pages) by R.E. Deakin, M.N. Hunter and C.F.F. Karney on the Transverse Mercator (Gauss-Krueger) projection and the Karney-Krueger equations. This paper was presented at the Surveying and Spatial Sciences Institute (SSSI) Land Surveying Commission National Conference, Melbourne, 18-21 April, 2012. This paper is an updated version of the Warrnambool Conference paper above.
A fresh look at the UTM projection – the Karney-Krueger equations V2.pdf
Map Projections, Mathematics and Computers
A technical paper (12 pages) describing how Computer Algebra Systems (CAS) are used to develop new equations for the Transverse Mercator projection. This paper was presented at the Geospatial Science Research_1 conference, Melbourne, 12-14 December, 2011.
MATHEMATICS AND MAP PROJECTIONS(GEOM2093).pdf
Tilted Camera map projection
Tilted Camera Map Projection.pdf
Transverse Mercator Projection: Karney-Krueger equations
These notes (12 pages) set out in detail the Forward and Inverse transformations between geographic coordinates (φ,λ) and grid coordinates (E,N) of the transverse Mercator projection of the ellipsoid using the Karney-Krueger equations. Equations for Grid Convergence and Point Scale Factor are also given for both transformations. An Excel workbook has spreadsheets for both transformations
Karney-Krueger equations.pdf
Karney-Krueger.xlsx
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